AP EAMCET2015MathematicsComplex Number
( 1+ 8 -i 8 1+ 8 +i 8 )^8 is equal to
Options
- A1
- B-1
- C2
- D1 2
Correct answer
B. -1
Step-by-step solution
aligned & ( 1+ 8 -i 8 1+ 8 +i 8 )^8 & = ( 2 ^2 16 -2 i 16 16 2 ^2 16 +2 i 16 16 )^8 & = ( 2 16 ( 16 -i 16 ) 2 16 ( 16 +i 16 ) )^8 & = ( 16 -i 16 16 +i 16 )^8 & = ( e^ - 16 i e^ 16 i )^8 & aligned array lr = (e^ - 2 16 i )^8 & [Using eular's theorem] = (e^ -8 2 16 i ) & [Using De-Moivre's theorem] array aligned & =e^ - i & = -i & =-1 aligned